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Wajsberg algebras.

Josep M. Font, Antonio J. Rodríguez, Antoni Torrens (1984)

Stochastica

We present the basic theory of the most natural algebraic counterpart of the ℵ0-valued Lukasiewicz calculus, strictly logically formulated. After showing its lattice structure and its relation to C. C. Chang's MV-algebras we study the implicative filters and prove its equivalence to congruence relations. We present some properties of the variety of all Wajsberg algebras, among which there is a representation theorem. Finally we give some characterizations of linear, simple and semisimple algebras....

Weak alg-universality and Q -universality of semigroup quasivarieties

Marie Demlová, Václav Koubek (2005)

Commentationes Mathematicae Universitatis Carolinae

In an earlier paper, the authors showed that standard semigroups 𝐌 1 , 𝐌 2 and 𝐌 3 play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by 𝐌 2 and 𝐌 3 are neither relatively alg-universal nor Q -universal, while there do exist finite semigroups 𝐒 2 and 𝐒 3 generating the same semigroup variety as 𝐌 2 and 𝐌 3 respectively and the quasivarieties generated by 𝐒 2 and/or 𝐒 3 are quasivar-relatively f f -alg-universal and Q -universal...

Weak congruences of an algebra with the CEP and the WCIP

Andrzej Walendziak (2002)

Czechoslovak Mathematical Journal

Here we consider the weak congruence lattice C W ( A ) of an algebra A with the congruence extension property (the CEP for short) and the weak congruence intersection property (briefly the WCIP). In the first section we give necessary and sufficient conditions for the semimodularity of that lattice. In the second part we characterize algebras whose weak congruences form complemented lattices.

Weak products of universal algebras

Ildikó Sain (1993)

Banach Center Publications

Weak direct products of arbitrary universal algebras are introduced. The usual notion for groups and rings is a special case. Some universal algebraic properties are proved and applications to cylindric and polyadic algebras are considered.

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